Grade 7 - Mathematics9.46 Area of Rectangular Path - III

Example:
A path of uniform width runs around and outside a square plot of side 20 metres. If the area of the path is 276 square metres find its width.

Solution:
Let the width of the path be x metres.
Now each side of the given square plot = 20 metres.
Therefore, each side of the outer square = (20 + 2x) metres, because the path runs outside.The are of the path = (The area of outer square) - (The area of the inner square)
= (20 + 2x)2 - 202
But the area of the path is given to be 276 square metres.
Therefore, (20 + 2x)2 - 202 = 276
(20 + 2x)2 = 202 + 276
(20 + 2x)2 = 400 + 276
(20 + 2x)2 = 676
Take square roots on both sidesÖ(20 + 2x)2 = Ö676
20 + 2x = 26
2x = 26 - 20
2x = 6
x = 6/3\ The width of the path = 3 metres.

Directions: Read the above example carefully and answer the following questions:

Draw a square plot of side 12 centi-metres and label its sides. Draw a path of uniform width around and outside the square plot. If the area of the path is given by 256 square centi-metres, then find the width of the path. Use different colors to represent the path and the square plot.

Q 1: A path of uniform width 4 metres runs around and outside a square plot. If the area of the path is 448 square metres find a side of the square plot.30 metres24 metres35 metres45 metres

Q 2: A path of uniform width 2 metres runs around and outside a square plot of side 22 metres. find the area of the path.192 square metres105 square metres100 square metres205 square metres

Q 3: A path of uniform width runs around and outside a square plot of side 15 metres. If the area of the path is 400 square metres find its width.5 metres4 metres2 metres3 metres

Q 4: A path of uniform width runs around and outside a square plot of side 25 metres. If the area of the path is 399 square metres find its width.3 metres3.5 metres2.5 metres2 metres